1. Field of the Invention
This invention relates to a current measuring device for measuring electrical current waveforms using a combination of a Rogowski coil and electronic processing equipment. In particular, this invention relates to improvements in such a device whereby the high frequency bandwidth of the measurement is increased whilst still retaining the capability of measuring low frequency currents.
2. Description of Related Art
A Rogowski coil is so named following publication in 1912 of an article titled xe2x80x9cDie Messung der Magnitischen Spannungxe2x80x9d (Arch Elektrotech1, pp141-150) by Rogowski W. and Steinhaus W. Its principle of operation is well known and is based on the fact that if a coil of uniformly spaced turns, wound is on a former of constant cross-sectional area, is arranged to form a closed loop, then the voltage induced in the coil at any instant is directly proportional to the rate of change of the total current passing through the loop at that instant. If means can be found of integrating with respect to time the voltage produced by the coil then the voltage obtained is proportional to the current passing through the loop. The combination of a Rogowski coil and means for integrating a voltage with respect to time thereby constitutes a current measuring system commonly referred to as a Rogowski transducer.
In practice there will be some small variation of the turns density of the coil and of the cross sectional area of the former. As a result the voltage produced by the coil will be slightly dependent on the position of the current in relation to the Rogowski coil loop. It is understood that reference in this specification to a Rogowski coil includes these practical tolerances.
The former around which the coil is wound is normally non-magnetic but it may be magnetic provided that the relative permeability of the magnetic material used is sufficiently small such that the material does not magnetically saturate when used to carry a Rogowski coil.
A Rogowski transducer has the advantages that the coil may be looped around a conductor, without the necessity of disconnecting the conductor; to provide a contactless and isolated current measurement and that large currents can be measured without magnetically saturating the transducer. A further advantage is that due to the use of non-magnetic material (which does not suffer from energy losses that increase with frequency), a Rogowski transducer potentially has a very high bandwidth, significantly in excess of 1 MHz and is therefore able to measure very rapidly changing currents.
Examples of known Rogowski transducers are described in the publications by Ray W F and Davis R M: xe2x80x9cWideband Rogowski current transducers: Part 1xe2x80x94The Rogowski Coilxe2x80x9d, EPE Journal, Vol 3, No.1, March 1993, pp 51-59, and Ray W F: xe2x80x9cWideband Rogowski current transducers: Part 2 xe2x80x9cThe Integratorxe2x80x9d, EPE Journal, Vol 3, No.2, June 1993, pp116-122.
The means for integrating the Rogowski coil voltage with respect to time may take various forms, some called xe2x80x9cpassivexe2x80x9d means in as much as the means only utilises passive electrical components such as capacitors and resistors. Others are called xe2x80x9cactivexe2x80x9d means in that the means also utilises active electronic components, such as semi-conducting devices and integrated circuits.
FIG. 1 shows a Rogowski current transducer that was proposed by J. A. J. Pettinga and J. Siersema in their paper xe2x80x9cA polyphase 500 kA current measuring system with Rogowski coilsxe2x80x9d, Proc IEE, Vol 130, Pt B, No. 5, September 83, pp 360-363. This measuring system incorporates two types of passive integration, which is relevant at high frequencies, and integration using a conventional non-inverting operational amplifier, which is called xe2x80x9cactivexe2x80x9d integration, for low frequencies.
In the circuit of FIG. 1, A represents the coil with distributed inductance L and capacitance C. The coil is connected to the remainder of the circuit by a co-axial cable terminated by a resistor RC of 50xcexa9, which is the characteristic impedance of the cable such that the terminating resistance seen by the coil is RC. The components R3, R4 and C2 comprise a passive integration network for which R3 greater than  greater than RC and R3 greater than  greater than R4. A non-inverting operational amplifier circuit D acts as an integrator at low frequencies and as a unity gain amplifier at high frequencies.
FIG. 2 shows the overall frequency characteristic for the integration which falls into three bandsxe2x80x94active integration for frequencies f in the range f0 less than f less than f1, passive CR integration for f1 less than f less than f2 and passive L/R integration for f greater than f2.
The resistors and capacitors of FIG. 1 are chosen such that for each frequency band the following behaviour occurs:
(a) The resistance R1 is relatively large and its presence is ineffective for frequencies f greater than f0.
(b) For f0 less than  less than f less than  less than f1 the impedance of L and the admittance of C2 are negligible and the voltage V+ at the non-inverting input of the operational amplifier is substantially the same as the voltage E induced in the coil. For integrator gains greater than 1 the behaviour of integrator D is represented by the well known relationship:                               V          out                =                              1                                          C                1                            ⁢                              R                2                                              ⁢                      ∫                          E              ⁢                              ⅆ                t                                                                        (        1        )            
(c) For f1 less than  less than f less than f2 the impedance of L and C1 are negligible and the circuit D acts as a unity gain amplifier. Since the impedance of R4 is also negligible, the network R3xe2x88x92C2 behaves as a passive integrator.
(d) For f greater than  greater than f2 circuit D continues to act as a unity gain amplifier and the impedance of C2 is negligible compared with that of R4. The network L-RC behaves as a passive L/R integrator. This is the type of integration that has been favoured in other known Rogowski transducers.
It will be appreciated that there are significant design constraints on the relative values for the resistors and capacitors used in order to provide the required transition of behaviour from one mode of integration to the next Furthermore, in order to provide a straight-line gain-frequency relationship for the integration as shown in FIG. 2 it is important that two pairs of time constants are accurately matched, namely                                           R            2                    ⁢                      C            1                          =                                            R              3                        ⁢                          C              2                        ⁢                          xe2x80x83                        ⁢            and            ⁢                          xe2x80x83                        ⁢                          L                              R                c                                              =                                    R              4                        ⁢                          C              2                                                          (        2        )            
The matching requirement presents difficulties both in the design and in the practical setting-up and calibration of a transducer. This is disadvantageous.
The circuit of FIG. 1 suffers from several additional disadvantages that have not until now been appreciated.
Firstly the circuit of FIG. 1 uses L/R integration. It is commonly thought that L/R integration does not result in unwanted signal oscillations. However, this is because previously published analysis of Rogowski transducers that utilise L/R integration is based on a symmetrical arrangement in which the coil loop is circular, the current to be measured lies along the axis of this circular loop and there are no other currents close to the coil. In this special case each element of the coil generates the same elemental voltage and the transit times from each element to the coil termination can be averaged to produce a smooth output voltage. The coil is therefore not susceptible to oscillations. As a result, L/R integration has been utilised in prior art transducers with satisfactory results provided care is taken to ensure a symmetrical geometry as described above. However, to utilise a symmetrical arrangement it is generally necessary to use a coil with a rigid former that cannot be opened and is therefore less convenient. Furthermore, when measuring currents in closely spaced equipment it is difficult and often impossible to arrange for the current to be central and co-axial with the coil loop. There are also often currents other than the current being measured which are close to the coil. In practice, therefore, the arrangement is not symmetrical. When this is the case, the coil is susceptible to oscillations. One solution that has been proposed is to design the coil so that its natural frequency is 4 to 5 times higher than the required bandwidth for the measured current. This solution has the disadvantage that the bandwidth of the measuring system is reduced by a factor of 4 to 5 times what could be achieved if L/R integration is not utilised.
Returning to the circuit of FIG. 1, this was designed for continuous sinusoidal currents with a bandwidth of only 100 kHz. With these specific limitations the possibility of coil oscillations (which are typically several MHz) is significantly reduced and this may enable L/R integration to be used. However for current waveforms with switching transients, such as for currents in power semi-conductors, high frequency harmonics exist which extend above 1 MHz and so cause oscillations.
In addition to L/R integration, the transducer of FIG. 1 also uses CR integration. It is known that circuits that use such integration can also suffer from the problem of unwanted oscillations One solution to this problem that has been proposed is to reduce the length of the cable connecting the coil and the CR part of the circuit.
It has only now been appreciated by the inventor of the invention described herein that high frequency oscillations in Rogowski transducers, such as those of FIG. 1, result from a mismatch between the characteristic impedance of the coil and the coil termination. This arises because the terminating resistance that is appropriate for the L/R integration of FIG. 1 is relatively small, typically 50 ohms or less, whereas the characteristic impedance of a Rogowski coil is typically 500 ohms or more. This mismatch of termination causes the output voltage to be subject to high frequency oscillations initiated by current changes in conductors outside the coil loop as well as the current being measured. Mismatch of the termination is inevitable in the circuit of FIG. 1.
A further disadvantage of the measuring system of FIG. 1 is that it does not enable both the Rogowski coil and the connecting cable to be separately terminated with the correct impedance. It will be seen in FIG. 1 that if the resistor RC is chosen to correctly terminate the cable then this resistance also becomes the terminating resistance for the coil. Therefore, unless the coil has the same characteristic impedance as the cable, the coil termination will be mismatched.
A yet further disadvantage of the measuring system of FIG. 1 is that the cable capacitance adds to the coil capacitance and so significantly reduces the bandwidth of the measurement system.
An object of the present invention is to provide a current transducer that overcomes the disadvantages of the prior art.
According to the present invention there is provided a current transducer comprising a Rogowski coil having an electrically conductive coil member with a coil termination, a first integrator connected across the coil termination and a second integrator connected to the output of the first integrator, the first integrator being arranged to have a substantially constant gain at relatively low frequencies and to integrate the coil output at relatively high frequencies and the second integrator being arranged to have a substantially constant gain at relatively high frequencies and to integrate the output of the first integrator at relatively low frequencies, wherein the Rogowski coil is terminated with a resistor or resistors in combination so as to provide a terminating resistance value that is approximately the same as the characteristic impedance of the coil, thereby damping the coil and reducing its susceptibility to high frequency voltage oscillations.
Since the coil terminating resistance is matched to the coil characteristic impedance, the coil inductance plays no part in the integration performed by either of the first or second integrators. This means that high frequency oscillations associated with L/R integration are avoided and the usable bandwidth of the transducer can be significantly extended. For example, the transducer in which the invention is embodied may have a bandwidth extending from 1 Hz to greater than 1 MHz.
Preferably, the first integrator is a passive integrator. Preferably, the second integrator is an active integrator.
Preferably, the passive integrator is a network of passive components. This may include the coil damping resistor.
Preferably the active integrator uses an operational amplifier in a non-inverting mode.
The frequency at which the first integrator ceases to operate as an integrator and commences to operate at a constant gain and the frequency at which the second integrator ceases to operate at a constant gain and commences to operate as an integrator may be set to be substantially the same.
The coil former may be a continuous ring made of plastic or some other suitable material and may be rigid or flexible. However, for ease of positioning the coil for use, it is preferable that the coil can be looped around a conductor without disconnecting the conductor, in which case the coil former needs to be discontinuous and of sufficiently flexible material that it can be bent into a loop around the conductor.
The passive integrator may comprise a resistor and a capacitor. An advantage of having the coil terminated with a resistance that is matched to the coil characteristic impedance in this instance is that it eliminates L/R integration and thereby avoids the difficulties of having to match CR and L/R time constants.
Preferably, the resistor and the capacitor are connected by a cable, the resistor being mounted at the coil end of the cable and the capacitor being at the second integrator end of the cable. An advantage of having the resistor at the coil end of the cable is that it avoids reducing the bandwidth of the transducer. Preferably, the resistor and the capacitor are in series.
The damping resistor may be connected at the coil end of the connecting cable such that it is in parallel with the resistor-capacitor combination of the passive integrator. Additionally, a second damping resistor may be connected between the second integrator end of the connecting cable and the capacitor of the passive integrator at that end. This second damping resistor preferably has a value substantially the same as the characteristic impedance of the connecting cable to provide a matched termination to the cable and to reduce the susceptibility of the cable to high frequency voltage oscillations.